Step |
Hyp |
Ref |
Expression |
1 |
|
isgbe |
|
2 |
|
2nn |
|
3 |
2
|
a1i |
|
4 |
|
oveq2 |
|
5 |
|
df-2 |
|
6 |
5
|
oveq2i |
|
7 |
|
1z |
|
8 |
|
fzpr |
|
9 |
7 8
|
ax-mp |
|
10 |
|
1p1e2 |
|
11 |
10
|
preq2i |
|
12 |
6 9 11
|
3eqtri |
|
13 |
4 12
|
eqtrdi |
|
14 |
13
|
oveq2d |
|
15 |
|
breq1 |
|
16 |
13
|
sumeq1d |
|
17 |
16
|
eqeq2d |
|
18 |
15 17
|
anbi12d |
|
19 |
14 18
|
rexeqbidv |
|
20 |
19
|
adantl |
|
21 |
|
1ne2 |
|
22 |
|
1ex |
|
23 |
|
2ex |
|
24 |
|
vex |
|
25 |
|
vex |
|
26 |
22 23 24 25
|
fpr |
|
27 |
21 26
|
mp1i |
|
28 |
|
prssi |
|
29 |
27 28
|
fssd |
|
30 |
|
prmex |
|
31 |
|
prex |
|
32 |
30 31
|
pm3.2i |
|
33 |
|
elmapg |
|
34 |
32 33
|
mp1i |
|
35 |
29 34
|
mpbird |
|
36 |
|
fveq1 |
|
37 |
36
|
adantr |
|
38 |
37
|
sumeq2dv |
|
39 |
38
|
eqeq1d |
|
40 |
39
|
anbi2d |
|
41 |
40
|
adantl |
|
42 |
|
prmz |
|
43 |
|
prmz |
|
44 |
|
fveq2 |
|
45 |
22 24
|
fvpr1 |
|
46 |
21 45
|
ax-mp |
|
47 |
44 46
|
eqtrdi |
|
48 |
|
fveq2 |
|
49 |
23 25
|
fvpr2 |
|
50 |
21 49
|
ax-mp |
|
51 |
48 50
|
eqtrdi |
|
52 |
|
zcn |
|
53 |
|
zcn |
|
54 |
52 53
|
anim12i |
|
55 |
7 2
|
pm3.2i |
|
56 |
55
|
a1i |
|
57 |
21
|
a1i |
|
58 |
47 51 54 56 57
|
sumpr |
|
59 |
42 43 58
|
syl2an |
|
60 |
|
2re |
|
61 |
|
3re |
|
62 |
|
2lt3 |
|
63 |
60 61 62
|
ltleii |
|
64 |
59 63
|
jctil |
|
65 |
35 41 64
|
rspcedvd |
|
66 |
65
|
adantr |
|
67 |
|
eqeq1 |
|
68 |
|
eqcom |
|
69 |
67 68
|
bitrdi |
|
70 |
69
|
anbi2d |
|
71 |
70
|
rexbidv |
|
72 |
71
|
3ad2ant3 |
|
73 |
72
|
adantl |
|
74 |
66 73
|
mpbird |
|
75 |
3 20 74
|
rspcedvd |
|
76 |
75
|
a1d |
|
77 |
76
|
ex |
|
78 |
77
|
rexlimivv |
|
79 |
78
|
impcom |
|
80 |
1 79
|
sylbi |
|